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An exact solution of the risk equation with a step current reserve function
Author(s):
D.
P.
Kerekesha
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 69
(2003).
Journal:
Theor. Probability and Math. Statist.
No. 69
(2004),
61-66.
MSC (2000):
Primary 62P05;
Secondary 42B30
Posted:
February 7, 2005
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Additional information
Abstract:
We obtain explicitly the solution of the risk equation for a step current reserve function.
References:
-
- 1.
- S. Asmussen, Ruin Probabilities, Advanced Series on Statistical and Applied Probability, World Scientific, Singapore, 2000. MR 1794582 (2001m:62119)
- 2.
- D. Kerekesha, Some generalization of the ruin probability problem in the classical risk theory, Theory Stoch. Process. 7(23) (2001), no. 2, 189-195.
- 3.
- P. Koosis, Introduction to
 Spaces, 2nd ed., Cambridge University Press, Cambridge, 1998. MR 1669574 (2000b:30052) - 4.
- N. I. Akhiezer, Lectures on Integral Transforms, ``Vyshcha Shkola'', Kharkiv, 1984; English transl., Amer. Math. Soc., Providence, RI, 1988. MR 0805538 (87c:44001)
- 5.
- L. Takács, Combinatorial Methods in the Theory of Stochastic Processes, Wiley, New York-London-Sydney, 1967. MR 0217858 (36:947)
- 6.
- V. A. Trenogin, Functional Analysis, ``Nauka'', Moscow, 1980. (Russian) MR 0598629 (82k:46001)
- 7.
- M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. 1, 2nd ed. Academic Press, New York, 1980. MR 0751959 (85e:46002)
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62P05,
42B30
Additional Information:
D.
P.
Kerekesha
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
DOI:
10.1090/S0094-9000-05-00614-9
PII:
S 0094-9000(05)00614-9
Received by editor(s):
14/OCT/2002
Posted:
February 7, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
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